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\((n,m)\)-SG rings. (English) Zbl 1219.16014

Summary: This paper is a continuation of [the author, Int. Electron. J. Algebra 6, 119-133 (2009; Zbl 1196.16006)]. Namely, we introduce and study a doubly filtered set of classes of rings of finite Gorenstein global dimension, which are called \((n,m)\)-SG for integers \(n\geq 1\) and \(m\geq 0\). Examples of \((n,m)\)-SG rings, for \(n=1\) and 2, and every \(m\geq 0\), are given.

MSC:

16E65 Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)
16E05 Syzygies, resolutions, complexes in associative algebras
16E10 Homological dimension in associative algebras
16E30 Homological functors on modules (Tor, Ext, etc.) in associative algebras

Citations:

Zbl 1196.16006